A covering property with respect to generalized preopen sets
Resumen
In this paper, we introduce and study the notion of $\mu$-precompact spaces on the observation that each $\mu$-preopen set of a generalized topological space is contained in a $\mu$-open set. The $\mu$-precompactness is weaker than $\mu$-compactness but stronger than weakly $\mu$-compactness of generalized topological spaces.Descargas
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D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38 (1986), 24–32.
A. Csaszar, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (1-2) (2005), 351–357.
A. Csaszar, Extremally disconnected generalized topologies, Ann. Univ. Sci. Budapest. E¨otv¨os Sect. Math. 47 (2004), 91–96.
A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (4) (2002), 351–357.
A. Csaszar, γ-compact spaces, Acta Math. Hungar. 87 (1-2) (2000), 99–107.
A. Csaszar, Generalized open sets, Acta Math. Hungar. 75 (1–2) (1997), 65–87.
I. Dochviri and J. F. Peters, Topological sorting of finitely near sets, Math. Comput. Sci. 10 (2) (2016), 273–277.
I. Dochviri and T. Noiri, Some remarks on mildly compact spaces in bitopologies, Questions Answers Gen. Topology 32 (1) (2014), 69–72.
M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mapping, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt 53 (1982), 47–53.
A. Mukharjee and R. M. Roy, Unification of maximality and minimality of open and µ-open sets, Bull. Transilv. Univ. Bra¸sov Ser. III 9(58) (2016), 83–90.
O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961–970.
T. Noiri, Unified characterizations of modifications of R0 and R1 topological spaces, Rend. Circ. Mat. Palermo (2) 55 (2006), 29–42.
M. S. Sarsak, µ-S-closed spaces, Acta Math. Hungar. 146 (2) (2015), 285–299.
M. S. Sarsak, On µ-compact sets in µ-spaces, Questions Answers Gen. Topology 31 (2013), 49–57.
M. S. Sarsak, Weakly µ-compact spaces, Demonstr. Math. 45 (4) (2012), 929–938.
T. Thomphson, S-closed spaces, Proc. Amer. Math. Soc. 60 (1976), 335–338.
S. Willard, General Topology, Addison-Wesley Publishing Company, Reading, 1970.
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